You might want to double check the native VLAN setting between your cisco and HP switch. We had a problem where there was a native vlan mismatch between a Juniper switch and a cisco switch and it caused an STP loop which caused a network outage.

The rest of your configuration looks fine, it's best practise to make the core switches the STP root bridges, so give them a low STP priority. I'm not sure what you are menioning when you refer to root priority of cisco switches being 0. Do you mean the port priorities? The main thing you want is the root bridge to be elected to be the HP switches. So make sure that the STP priority are lower than the cisco ones. Not higher - the bridge-id is made up of a bridge priority (which you can configure) and the MAC address of the switch.

The trunking configuration looks good, on the cisco side you can set the trunk to be either desirable (actively negotiates LACP) or auto (passive - therefore responds to active requests for LACP bundle)

I was reading a document on A58xx switches and other switches. A58xx uses IRF / LACP instead of xSTP but when you connect them to non-HP A58xx switches, you need to configure an STP protocol. I was looking at this because I want to use a Cisco ASA-5520 for secondary routes and use A58xx VLAN to VLAN for primary routes.

Thank you for your response and sorr for typing it again. I will double check the native VLANs to be the same at both Cisco and HP. By default, both Cisco and HP have native VLAN of 1 but will make sure that nobody changed native VLAN on Cisco existing switches. If they did then I will match at the HP end as well.

Regarding Root Bridge, actually, we are not replacing Cisco Distrubiton Switches with HP. The Cisco 6513s will continue to be operate as distribution switches and shoulb be the root bridges. HP switches will act as server farm switches and will be connecting over (2) 10GB LACP to Cisco distribution switches. That is why I don't want HP switches to take over Cisco switches as root bridges. The root priorities on Cisco 6513s switches are set to 0 for certain VLANs and 4096 for other VLANs and Vice Versa on the 2nd set of 6513. Typical Cisco model for VLANs load balancing between two distribution switches.

I am very sure that by default HP root priorities are higher than 4096 so I won't have to change any settings there.

HP A5830 does support PVST mode and was wondering if I should turn on PVST instead of RSTP since Cisco 6513s are configured with PVST+

Last, not sure how HP switches will behave when it comes to root port or designated root port and wanted to find out if I need to manually configure the settings for root or desiganted root ports.